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The object 4C 71.07 is a high-redshift blazar whose spectral energy distribution shows a prominent big blue bump and a strong Compton dominance. We present the results of a 2- yr multiwavelength campaign led by the Whole Earth Blazar Telescope (WEBT) to study both the quasar core and the beamed jet of this source. The WEBT data are complemented by ultraviolet and X-ray data from Swift, and by γ-ray data by Fermi. The big blue bump is modelled by using optical and near-infrared mean spectra obtained during the campaign, together with optical and ultraviolet quasar templates. We give prescriptions to correct the source photometry in the various bands for the thermal contribution, in order to derive the non-thermal jet flux. The role of the intergalactic medium absorption is analysed in both the ultraviolet and X-ray bands.We provide opacity values to deabsorb ultraviolet data, and derive a best-guess value for the hydrogen column density of Nbest H = 6.3 × 10 cmthrough the analysis of X-ray spectra.We estimate the disc and jet bolometric luminosities, accretion rate, and black hole mass. Light curves do not show persistent correlations among flux changes at different frequencies. We study the polarimetric behaviour and find no correlation between polarization degree and flux, even when correcting for the dilution effect of the big blue bump. Similarly, wide rotations of the electric vector polarization angle do not seem to be connected with the source activity.© 2019 The Author(s)., We acknowledge financial contribution from the agreement ASI-INAF n.2017-14-H.0 and from the contract PRIN-SKA-CTA-INAF 2016. PR and SV acknowledge contract ASI-INAF I/004/11/0. We acknowledge support by Bulgarian National Science Programme 'Young Scientists and Postdoctoral Students 2019', Bulgarian National Science Fund under grant DN18-10/2017 and National RI Roadmap Projects DO1-157/28.08.2018 and DO1-153/28.08.2018 of the Ministry of Education and Science of the Republic of Bulgaria. GD and OV gratefully acknowledge the observing grant support from the Institute of Astronomy and Rozhen National Astronomical Observatory, Bulgarian Academy of Sciences via bilateral joint research project 'Study of ICRF radio-sources and fast variable astronomical objects' (head -G.Damljanovic). This work is a part of the Projects No. 176011 ('Dynamics and Kinematics of Celestial Bodies and Systems'), No. 176004 ('Stellar Physics'), and No. 176021 ('Visible and Invisible Matter in Nearby Galaxies: Theory and Observations') supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia. This research was partially supported by the Bulgarian National Science Fund of theMinistry of Education and Science under grants DN 08-1/2016, DN 18-13/2017, and KP-06-H28/3 (2018). The Skinakas Observatory is a collaborative project of the University of Crete, the Foundation for Research and Technology -Hellas, and the Max-Planck-Institut fur Extraterrestrische Physik. The St Petersburg University team acknowledges support from Russian Science Foundation grant no. 17-12-01029. The Abastumani team acknowledges financial support by the Shota Rustaveli National Science Foundation under contract FR/217950/16. This work was partly supported by the National Science Fund of the Ministry of Education and Science of Bulgaria under grant DN 08-20/2016, and by funds of the project RD-08-37/2019 of the University of Shumen. The Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA) is managed by the Fondazione Clement Fillietroz-ONLUS, which is supported by the Regional Government of the Aosta Valley, the Town Municipality of Nus and the Unite des Communes valdotaines Mont-Emilius'. The research at the OAVdA was partially funded by two 'Research and Education' grants from Fondazione CRT